# Boolean Algebra Calculator

Boolean algebra is a division of mathematics that deals with operations on logical values and incorporates binary variables.

## What is Boolean Algebra Calculator?

'Boolean Algebra Calculator' is an online tool that helps to calculate the truth tables for the given inputs. Online Boolean Algebra Calculator Calculator helps you convert calculate the truth tables for the given inputs in a few seconds.

## How to Use Boolean Algebra Calculator?

Follow these steps which will help you to use the calculator.

**Step 1**: Choose the boolean algebra from the drop-down list.**Step 2**: Click on the "**Show**" button to find the truth tables for the input.**Step 3**: Click on the "**Reset**" button to clear the field and choose the new boolean algebra.

## How to Find Boolean Algebra?

The Boolean variables are represented as binary numbers to represent truths i.e., 1 = true and 0 = false. Elementary algebra deals with numerical operations whereas Boolean algebra deals with logistical operations. There are different types of logic gates i.e., AND, OR, and NOR gates.

**Conjunction or AND gate:** Consider the statement “p and q”, denoted p∧q

**Rule1**: If 'p' and 'q' both statements are True then “p and q (p∧q)” is also a True statement.**Rule2**: If 'p' is False while 'q' is True then “p and q (p∧q)” is False. For “p and q” to be true, we would need Both statements to be True. Since one is false, “p and q” is False.**Rule3**: If 'p' is True while 'q' is False then “p and q (p∧q)” is False. For “p and q” to be true, we would need Both statements to be True. Since one is false, “p and q” is False.**Rule4**: If both the statements are False then “p and q” is False.

**Disjunction or OR gate: **Consider the statement “p OR q”

**Rule1**: If both the statements are True then "p or q” is also a True statement.**Rule2**: If 'p' is False while 'q' is True then “p or q” is True. Since one is True.**Rule3**: If 'p' is True while 'q' is False then “p or q” is True. Since one is True.**Rule4**: If both the statements are False then "p or q” is False.

**XOR gate:** Consider the statement “p XOR q”

**Rule1**: If both the statements are True then "p xor q” is False.**Rule2**: If 'p' is False while 'q' is True then “p xor q” is True.**Rule3**: If 'p' is True while 'q' is False then “p xor q” is True.**Rule4**: If both the statements are False then "p xor q” is False.

**NOR gate:** Consider the statement “p NOR q”

**Rule1**: If both the statements are True then "p nor q” is a False statement.**Rule2**: If 'p' is False while 'q' is True then “p nor q” is a False statement.**Rule3**: If 'p' is True while 'q' is False then “p nor q” is a False statement.**Rule4**: If both the statements are False then "p nor q” is a True statement.

**Negation or NOT gate: **Negation is the statement represented by ¬p, and so it would have the opposite Truth value of p. If p is True, then ¬p is False. If p is False, then ¬p is True.

**Solved Example:**

Find the possible truth tables for the p ∧ q

**Solution: **

Let p and q be the statements. Here 1 stand for True and 0 stands for False.

p q p ∧ q

1 0 0

0 1 0

1 1 1

0 0 0

Similarly, you can try the calculator to find the truth tables for:

- p ∧ q ¬p
- p v q ¬q